Calculators
Elliptical Frustum Calculator
Calculate right elliptical cone frustum volume, base areas, and top semi-axes from similar elliptical bases.
Calculate volume between similar elliptical bases.
A right elliptical cone frustum is a cone truncated by a plane parallel to its base. Enter bottom semi-axes a and b, perpendicular height h, and the top-to-bottom linear scale factor k. Both top semi-axes use the same factor: ka and kb. Bottom area A = πab; top area = Ak²; volume V = Ah(1 + k + k²)/3. For a = 5, b = 3, k = 0.5 and h = 4, volume is 35π ≈ 109.955742876 cubic units. Scale 0 gives a full elliptical cone and scale 1 gives an elliptical cylinder. Bases must be similar, parallel, centered and aligned. This calculator reports volume and flat base areas, not curved or total surface area. Use consistent length units; semi-axes and height must be from 1e-50 to 1e50, and k from 0 to 1. Scientific notation is accepted. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Why use one scale factor for both top semi-axes?
A cone cut parallel to its base produces similar ellipses. Both top semi-axes must have the same ratio to their bottom counterparts. Arbitrary top axes do not describe this shape.
Which volume formula is used?
V = πabh(1 + k + k²)/3, where a and b are bottom semi-axes, h is perpendicular height and k is the top linear scale factor. For 5, 3, 0.5 and 4 the volume is 35π cubic units.
Can I calculate a cone or cylinder?
Yes. Use scale 0 for a full elliptical cone or scale 1 for an elliptical cylinder. Equal bottom semi-axes give a circular cone frustum.
Does this include curved surface area?
No. Results include volume, flat base areas and derived top semi-axes. Curved and total surface areas are not calculated. Use consistent units. Calculations run locally in your browser.